Natural Hazards and Earth System Sciences Recent changes in the number of rainfall events related to debris-flow occurrence in the Chenyulan Stream Watershed , Taiwan

This study analyzed the variability in the number of rainfall events related to debris-flow occurrence in the Chenyulan stream watershed located in central Taiwan. Rainfall data between 1970 and 2009 measured at three meteorological stations nearby/in the watershed were collected and used to determine the corresponding regional average rainfall for the watershed. Data on debris-flow events between 1985 and 2009 were collected and used to study their dependence on regional average rainfall. The maximum 24-h regional rainfallRd was used to analyze the number of rainfall eventsNr, the number of rainfall events that triggered debris flowsNd, and the probability of debris-flows occurrencesP . The variation trends inNr, Nd and P over recent decades under three rainfall conditions ( Rd > 20,230, and 580 mm) related to debris-flow occurrence were analyzed. In addition, the influences of the Chi-Chi earthquake onNd andP were presented. The results showed that the rainfall events withRd > 20 mm during the earthquakeaffected period (2000–2004) strongly responded to the increases in the average number of rainfall events that triggered debris flows and the average probability of debris-flows occurrences. The number of rainfall events with Rd > 230 mm (the lower boundary for the rainfall ever triggering debris flow before the Chi-Chi earthquake), and Rd > 580 mm (the lower boundary for extreme rainfall ever triggering numerous debris flows) in the Chenyulan stream watershed increased after 2000. The increase in the number of extreme rainfall events withRd > 580 mm augmented the number of rainfall events ever triggering numerous debris flows in the last decade. The increase in both the number of rainfall events that ever triggered debris flows and the probability of debrisflow occurrences was greater in the last decade (2000–2009) than in 1990–1999.


Introduction
Over the past few decades, global climate change has caused a series of changes (Katz and Brown, 1992;IPCC, 1996;Bryant, 1997), including increase in precipitation and temperature and more frequent natural disaster events; climate change has become one of the world's most critical issues.Some previous studies have examined the impact of climate change on debris-flow activity in mountainous areas.For example, Zimmermann and Haeberli (1992) analyzed the relationship between climate variation and debris flows in the Swiss Alps.Rebetez et al. (1997) recorded debris-flow events in Ritigraben in the Swiss Alps, and studied the longterm impact of temperature and rainfall fluctuations on the frequency of debris-flow events.Jomelli et al. (2004) analyzed the effects of climate change on the frequency and altitude of debris-flow events in recent decades in Dévoluy and Ecrins in the French Alps.Stoffel (2007) investigated the variability that may be caused in debris-flow occurrence under future greenhouse climate conditions in the area of Ritigraben in the Alps.These studies showed some relationships between debris-flow triggers and (1) an increase in the number of intense rainfall events and/or (2) glacier retreat and permafrost degradation due to an increase in temperatures.However, the hydrologic response of debris flows to climate is complex (Jakob and Lambert, 2009).The relationships between rainfall changes and debris-flow occurrences differ regionally since there are differences in regional responses to global climate change.Rainfall change generally responds to variations in the number of specified rainfall events with rainfall amount greater than a certain threshold.The present study investigated the relationship between the variability in specified rainfall events and debris-flow occurrence in the Chenyulan stream watershed, where many debris-flow events have been recorded since 1985.One objective of this work was to understand variations in regional rainfall characteristics, such as the number of rainfall events for a certain rainfall amount, and their relation to debris-flow occurrences in the Chenyulan stream watershed in recent decades; the second objective was to determine whether the number of rainfall events that triggered debris flows and the probability of debris-flow occurrences in the Chenyulan stream watershed were affected by variations in regional rainfall characteristics.Furthermore, empirical relationships were presented for the average annual number of rainfall events triggering debris flows and the probability of debris-flow occurrences relative to the average annual number of rainfall events in the past decades.The results of this study can provide a scientific basis for the long-term forecast and prevention of debris flows.

Debris flows in the Chenyulan stream watershed
The Chenyulan stream watershed, located in Nantou County in central Taiwan, has a catchment area of 449 km 2 , a main stream length of 42 km, a mean stream gradient of 4 • , and elevations between 310 and 3952 m.The Chenyulan stream follows the Chenyulan Fault, a boundary fault dividing two major geological zones of Taiwan.In addition to the boundary fault, the Chenyulan stream watershed also contains many other faults accompanied by fracture zones.Consequently, fractured rock masses prevail within the study area, accounting for enormous landslides and providing an abundant source of rock debris for debris flows (Lin and Jeng, 2000).The annual rainfall in the watershed ranges from 2000 mm to 5000 mm, with an average value of approximately 3500 mm.Approximately 80 % of the annual rainfall in the watershed occurs between May and October, especially during typhoons.Debris-flow hazards are common within the watershed, owing to the combination of weak geological conditions, heavy rainfall, and accompanying frequent earthquakes.Several debris-flow events in this watershed have been studied or documented (Lin and Jeng, 2000;Chang et al., 2001;Cheng et al., 2005;Jan and Chen, 2005;Chen and Jan, 2008;Chen et al., 2009;Chen, 2011;Chen et al., 2011).The present study utilized hydroclimatic data for events inducing debris flows from 1985 to the end of 2009.
Thirty-six rainfall events, including 18 rainstorms and 18 typhoon-induced heavy rainfall events, have caused debris flows in the Chenyulan stream watershed, as listed in Table 1.Notably among these, heavy rainfall events were associated with Typhoon Herb in 1996, Typhoon Toraji in 2001, and Typhoon Morakot in 2009.Typhoon Herb struck Taiwan between 31 July and 1 August 1996.The typhoon caused an unexpectedly high cumulative rainfall (up to 1994 mm within 2 days, measured at Alisan rainfall station near the headwater of the watershed) and caused over thirty debris-flows (Jan and Chen, 2005); 27 people were declared dead and 14 missing.The 1999 Chi-Chi earthquake with a moment magnitude M w = 7.6, on 21 September 1999, was the largest in Taiwan for 50 yr and the largest on the Chelungpu thrust fault in 300-620 yr (Shin and Teng, 2001;Chen et al., 2001;Dadson et al., 2004;Huang et al., 2001) and caused significant effects on the watershed.After the Chi-Chi earthquake, the extremely heavy rains brought by Typhoons Toraji and Nali in 2001 caused numerous debris flow events in central Taiwan (Cheng et al., 2005), and resulted in over 100 people dead or missing and major damage to houses, roads, bridges, and dikes.In August 2009, Typhoon Morakot brought heavy rainfall with an hourly rainfall up to 123 mm and a 48-h cumulative rainfall up to 2361 mm, as measured at Alisan rainfall station.It caused many debris flow events and other damage such as failure of river embankments, collapsed bridges, buried houses, and damage to numerous sections of Highway Route 21.In Shenmu and Tongfu villages in Xinyi Township, over 20 houses were buried by debris flows or washed away by floods.Numerous debris-flow events triggered by rainstorms and typhoons between 1985 and 2009 (as listed in Table 1) provide an opportunity to study the variability in the number of specified rainfall events associated with debrisflow occurrences in the Chenyulan stream watershed.

Regional average rainfall in the Chenyulan stream watershed
The trend in regional rainfall characteristics in the Chenyulan stream watershed needs to be studied by estimating the long-term record of rainfall data.As shown in Fig. 1, there are three meteorological stations -Sun Moon Lake, Yushan, and Alisan -near/within the Chenyulan stream watershed where rainfall data series have been collected for more than 40 yr (since 1970).Therefore, the hourly rainfall data collected from these three stations between 1970 and 2009 were used to estimate the regional average rainfall p for the watershed by using the reciprocal-distance-squared method (Chow et al., 1988).Since this method is simple and can directly reflect the weighting of distance, it has been widely used not only in determining ungauged or regional average rainfalls but also in determining unmeasured or regional average physical quantities in other fields, such as hydrology and earth science (Ashraf et al., 1997;Cheng, 1998;Teegavarapu and Chandramouli, 2005;Chen, 2011).The regional average rainfall estimated by the reciprocal-distance-squared method can be expressed as follows: where p i is the rainfall record from meteorological stations, and i = 1, 2, or 3 represents the Sun Moon Lake, Yushan, or Alisan meteorological stations, respectively; w i is the weighting factor corresponding to p i .The weighting factor is expressed as Note: N = total number of individual debris flow triggered by each rainfall event in the Chenyulan stream watershed; I m = maximum hourly rainfall in each rainfall event; R d = maximum 24-h rainfall amount in each rainfall event; R = total rainfall calculated from the start of rainfall to the end of rainfall; T = rainfall duration corresponding to estimate total rainfall R; I = mean rainfall intensity, I = R/T .
from the meteorological station i to the centroid of the considered watershed.In the study, the weighting factors w 1 ,w 2 , and w 3 are 0.099, 0.387, and 0.514, respectively.
The rainfall characteristics estimated by the reciprocaldistance-squared method may not actually reflect the rainfall characteristics at specific locations when local rainfall varied significantly owing to abrupt changes in elevation, but it is a simple method to directly compute the regional average rainfall characteristics for a watershed.The regional average rainfall in the Chenyulan stream watershed was computed by Eq. ( 1) on the basis of the hourly rainfall records from the three meteorological stations.In the Chenyulan stream watershed, rainstorms, thundershowers, and typhoons occur frequently during the rainy season, from May to October.Most debris flows, in particular those associated with typhoons, occur in the rainy season.Typhoons generally bring heavy rainfall and result in significant debris flows in the watershed.
The five-year-moving-average variations in the annual rainfall and the rainy-season rainfall at the three meteorological stations and the corresponding regional average rainfall in the Chenyulan stream watershed are presented in Fig. 2a  and b.The average annual rainfall in the watershed is between 2500 mm and 4500 mm, with an average value of  The variation in the regional average rainfall shows a trend similar to the rainfall measured at the three rainfall stations.The results suggest that the regional average rainfall computed by Eq. ( 1) can reasonably represent the variation trend of the regional rainfall characteristics in the entire Chenyulan stream watershed; hence, the reciprocal-distance-squared method (Eq. 1) was used to analyze the recent changes in the regional average rainfalls related to debris-flow occurrences in the watershed.Table 1 lists the regional average rainfalls that triggered debris flows in the Chenyulan stream watershed between 1985 and 2009.The rainfall data for a rainfall event that triggered debris flows include the maximum hourly rainfall I m , the maximum 24-h rainfall R d , the accumulated rainfall R from the initiation of rainfall to the end of rainfall, the rainfall duration T (h) from rainfall initiation to the end of rainfall, and the average rainfall intensity I (mm h −1 ) defined as I = R/T .The number of debris flow events N is defined as the total number of individual debris flow triggered by each rainfall event in the Chenyulan stream watershed; the value of N triggered by a rainstorm or typhoon event is also mentioned in Table 1.Prior to 1996, the number of debris flows was collected from papers (Yu and Chen, 1987;Chiang and Lin, 1991;Chang et al., 2001) without covering the whole watershed due to lack of data from field investigations.After 1996, the number of debris flows was collected from related documents and papers (Lin and Jeng, 2000;Cheng et al., 2005;Jan and Chen, 2005;Chen et al., 2009;Chen, 2011) and identified through interpretations of aerial photographs and field investigations in the whole watershed.

The rainfall conditions of debris-flow occurrences
Previous researchers have used many rainfall parameters, including I m , R d , R, I , and T , to study the occurrence of debris flows.The choice of rainfall parameters adopted may vary according to different objectives.For example, empirical relationships between average rainfall intensity and rainfall duration have been proposed and generally used to issue debris-flow warnings (Caine, 1980;Keefer et al., 1987;Chen et al., 2005;Chen, 2011).I m and R d have been used to determine the rainfall conditions for debris-flow occurrence in an extreme rainfall event (Lin and Jeng, 2000;Cheng et al., 2005).The daily rainfall or 3-day rainfall in a rainfall event has been used to analyze the influence of climatic or rainfall change on debris-flow activity (Rebetez et al., 1997;Zhuang et al., 2011).
Debris-flow occurrence is strongly related to extreme rainfall events (Rebetez et al., 1997;Zhuang et al., 2011).R d is one of several simple indices representing extreme rainfall characteristics.Furthermore, it was found that debris flows initiated in the Chenyulan stream watershed were closely related to R d .All debris flows triggered by a rainfall event in the watershed was within the period of maximum 24-h rainfall.Thus, the present study used R d to analyze recent changes in the relationship between the number of specified rainfall events and debris-flow occurrence.Figure 3 shows the values of R d for rainfall events that triggered debris flows during the data series .It is clear that the lowest values of R d that triggered debris flows were recorded during the period 2000 to 2004.Therefore, it is believed that the influence of the 1999 Chi-Chi earthquake on debris flow initiation lasted approximately 5 yr (Chen, 2011).Three critical rainfall conditions for debris-flow occurrence were imposed on Fig.  :R d > 20 mm 2000-2004 1995-1999 2005-2009 1990-1994 1985-1989 Figure 5: Relationship between five-year-average for rainfall events that triggered debris flow 5 d N and five-year-average number of rainfall events 5 r N with maximum 24-h rainfall greater than 20 mm.

P5
:R d > 20 mm 2000-2004 1995-1999 2005-2009 1990-1994 1985-1989 Figure 6: Relationship between the five-year-average probability of debris-flow occurrence 5 P and the five-year-average number of rainfall events 5 r N with maximum 24-h rainfall greater than 20 mm.Fig. 5. Relationship between five-year-average number of rainfall events that triggered debris flows N d5 and five-year-average number of rainfall events N r5 with maximum 24-h rainfall greater than 20 mm.watershed (1970 to 2009) ranges from 8 to 34 (average 21.7), but without a clearly increasing or decreasing trend.Figure 4b shows that the annual number (N d ) of rainfall events that triggered debris flows is between 0 and 9, with larger numbers occurring between 2000 and 2002 owing to the influence of the Chi-Chi earthquake, which provided the loose sediment required for debris-flow occurrence (Lin et al., 2003;Chen, 2011).Figure 4c shows the annual average probability P (= N d /N r ) of debris-flow occurrence for rainfall events having R d > 20 mm is less than 48 %; there was an abrupt increase after Typhoon Herb in 1996, and the peak value was observed in the year 2000 immediately after the Chi-Chi earthquake since Typhoon Herb and the Chi-Chi earthquake resulted in large amounts of loose sediment in catchments (Lin and Jeng, 2000;Lin et al., 2003).After 2000, both N d and P decreased slowly because the loose sediment became more consolidated and re-orientated with time, less soil and rock was deposited in streams after each storm, and the shear strength of soil gradually recovered (Fan et al., 2003;Chen, 2011).In response, the amount of rainfall required to trigger a debris flow gradually increased and the values of N d and P for the same rainfall condition (R d > 20 mm) decreased with time.Figure 4c shows that the value of P before the Chi-Chi earthquake was generally less than 10 %, which is the same as that after 2004.This implies that the probability of debris-flow occurrence after 2004 reverted to the pre-earthquake condition.The influence of the Chi-Chi earthquake on debris flow initiation was substantial during the period 2000-2004.This finding is consistent with a previous study by Chen (2011).
Figures 5 and 6 show the relationship between the fiveyear-average for rainfall events triggering debris flows Nd5 and the five-year-average number of rainfall events Nr5 ; also shown is the relationship between the probability of debrisflows occurrences in a five-year period P5 (= Nd5 / Nr5 ) and Nr5 for the condition-A rainfall events.The values of Nd5 and P5 during the Chi-Chi earthquake-affected period (2000)(2001)(2002)(2003)(2004) were significantly greater than those during other

P5
:R d > 20 mm 2000-2004 1995-1999 2005-2009 1990-1994 1985-1989 7 Figure 6: Relationship between the five-year-average probability of debris-flow occurrence 8 5 P and the five-year-average number of rainfall events 5 r N with maximum 24-h rainfall 9 greater than 20 mm. 10 11 12 Fig. 6.Relationship between the five-year-average probability of debris-flow occurrence P 5 and the five-year-average number of rainfall events N r5 with maximum 24-h rainfall greater than 20 mm.   8. Relationship between the five-year-average number of rainfall events that ever triggered debris flows N d5 and the five-yearaverage number of rainfall events N r5 for rainfall events having maximum 24-h rainfall larger than 230 mm.periods.The value of Nd5 in the earthquake-affected period is 3.8 times that during the five-year period pre-earthquake (1995)(1996)(1997)(1998)(1999); the probability of debris-flow occurrences ( P5 ) in the earthquake-affected period is 5.5 times that during the five years pre-earthquake; in particular, the Nr5 (2000Nr5 ( -2004) ) is less than Nr5 (1995Nr5 ( -1999)).The condition-A rainfall events (R d > 20 mm) during the earthquake-affected period strongly responded to the increases in Nd5 and P5 , especially within the period (2000)(2001)(2002)(2003)(2004) of the lowest number of rainfall events.

Condition B: Rainfall events with R d > 230 mm
Before the Chi-Chi earthquake, debris flows generally occurred when R d > 230 mm. Figure 7a and b shows that the number of rainfall events with R d > 230 mm that have high values of N r > 2 was concentrated in the period of 2004 and 2008, and the number of rainfall events that triggered debris flows was highest between 2004 and 2008.However, the highest value of N d in the period 2004-2008 may not correspond to the highest probability of debris-flows occurrence since the probability of debris-flow occurrence was the lowest for the rainfall events in 2004 and 2005 (Fig. 7c).This result may be attributed to the fact that during the period 2004-2005, the large amount of loose sediments attributed to the 1999 Chi-Chi earthquake decreased after Typhoon Toraji (Lin et al., 2003) and after the earthquake-affected period (Chen, 2011); furthermore, this result may be also attributed to insufficient loose sediment generated by each rainfall event in 2004 and 2005.Because a large amount of loose sediment is required for debris-flows occurrence, the probability of debris-flow occurrence decreased.Beginning in 2006, the probability of debris-flows occurrence increased; this may be due to a large amount of loose sediment accumulated or generated in the Chenyulan stream watershed.The annual rainfall event with R d > 580 mm that ever triggered numerous debris-flows occurred annually after 2006.
Figure 8 shows the relationship between the five-yearaverage number ( Nd5 ) of rainfall events of R d > 230 mm P for rainfall events having maximum24-h rainfall larger than 580 mm.14 15 16 5 Fig. 9. Number of annual rainfall events N r , number of rainfall events N d that triggered debris flows, and annual average probability of debris-flow occurrence P for rainfall events having maximum 24-h rainfall larger than 580 mm. that triggered debris flows and the five-year-average number ( Nr5 ) of rainfall events of R d > 230 mm.The five-yearaverage of rainfall events triggering debris flows ( Nd5 ) increased with the increase in the five-year-average number of rainfall events.

Condition C: rainfall events with R d > 580 mm
The number (N r ) of rainfall events of R d > 580 mm during 1970-2009 is shown in Fig. 9a.There are seven rainfall events with R d > 580 mm.This magnitude of rainfall event first occurred in 1996, followed by 2001 (5 yr later), 2004 (3 yr later), 2006 (2 yr later), and then occurred almost annually.All rainfall events, including six typhoons and one rainstorm, of R d > 580 mm resulted in debris flows and these rainfall events resulted in a 100 % probability of debris-flows www.nat-hazards-earth-syst-sci.net/12/1539/2012/Nat.Hazards Earth Syst.Sci., 12, 1539-1549, 2012 Year (c) Annual average probability of debris-flow occurrence P for rainfall events having maximum 24-h rainfall larger than 580 mm. Figure 9: Number of annual rainfall events Nr , number of rainfall events Nd that triggered debris flows, and annual average probability of debris-flow occurrence P for rainfall events having maximum24-h rainfall larger than 580 mm.: R d > 580 mm 2000-20041995-19992005-20091985-1989& 1990-1994 Figure 10: Figure 10: Relationship between the five-year-average number of rainfall events that triggered debris flows 5 d N and the five-year-average number of rainfall events 5 r N for rainfall events having maximum 24-h rainfall larger than 580 mm.Fig. 10.Relationship between the five-year-average number of rainfall events that triggered debris flows N d5 and the five-year-average number of rainfall events N r5 for rainfall events having maximum 24-h rainfall larger than 580 mm.occurrence (Fig. 9b and c).The three typhoons, Herb, Toraji and Morakot, caused many debris flows (N > 30).In particular, Typhoon Toraji (2001) resulted in more than 60 debrisflow events in the Chenyulan stream watershed, despite having lower rainfall (R d = 588 mm) than the other six rainfall events with R d > 580 mm.The high number of debris-flows N occurring during Typhoon Toraji is inferred to be related to the occurrence of this event during the Chi-Chi earthquake affected period (2000)(2001)(2002)(2003)(2004) when abundant loose sediment derived from the earthquake was present in the watershed.
Figure 10 shows the five-year average number ( Nd5 ) for rainfall events triggering debris flows against the five-year average number ( Nr5 ) for rainfall events.As all rainfall events with R d > 580 mm triggered debris flows, the number of such rainfall events triggering debris flows Nd5 was perfectly correlated with the five-year average for the number of rainfall events Nr5 for the condition-C rainfall events.The five-year average number of rainfall events triggering debris flows ( Nd5 ) increased with the higher five-year average number of rainfall events.As seen in Fig. 10, both Nd5 and Nr5 also showed increasing trends after 1990.
5 Variations in rainfall events triggering debris flows and the probability of debris-flow occurrence in each decade

Variations in the number of rainfall events
Figure 11 shows variations in the ten-year average for rainfall events N r10 , with R d larger than various rainfall thresholds R dc for two separate decades 1990-1999 and 2000-2009.The number of rainfall events for R d > 100 mm at various values of R dc during the period 1990-1999 is less than that in 2000-2009.For larger R dc , the value of N r10 in 2000-2009 is significantly larger than that in 1990-1999.This implies that there were more extreme rainfall events in the recent decade (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009).The value of N r10 for the condition-A rainfall event (R d > 20 mm) during 2000-2009 was around 10 % less than that in 1990-1999.The values Relationship between the ten-year-average number of rainfall events that triggered debris flows N d10 and the ten-year-average number of rainfall events N r10 with R d greater than various rainfall thresholds R dc , such as R dc = 20, 100, .., and 580 mm, during the periods 1990-1999 and 2000-2009. of N r10 for the rainfall events during 2000-2009 were 1.8 (condition B) and 6 (condition C) times the corresponding values in 1990-1999.Owing to the variation in the number of rainfall events in the past two decades, the influence of the variation in the number of rainfall events relative to debris flows and the probability of debris-flow occurrence were analyzed in the following sections.

The relationship between the number of rainfall events triggering debris flows and the number of rainfall events
Figure 12 shows the relationship between the ten-year average number of rainfall events triggering debris flows Nd10 and the ten-year-average number of rainfall events Nr10 at  13. Relationship between the ten-year-average probability of debris-flow occurrence P 10 and the ten-year-average number of rainfall events N r10 with R d greater than various rainfall thresholds R dc , such as R dc = 20, 100, .., and 580 mm, during the periods 1990-1999 and 2000-2009.various rainfall conditions of R d > R dc for two periods: 1990-1999 and 2000-2009.The values of Nd10 in both periods increase with decreasing rainfall thresholds R dc .For the period 1990-1999 and 2000-2009, larger rainfall thresholds R dc are generally associated with lower Nr10 and correspond to lower Nd10 .Figure 12 shows that the value of Nd10 during 2000-2009 was greater than that during 1990-1999 at the same rainfall thresholds of R dc .As indicated by the solid circle symbols shown in Fig. 12, the number of rainfall events that triggered debris flows Nd10 for the condition-B rainfall events (R d > 230 mm) during 2000-2009 was around 3 times that in 1990-1999; for the condition-A (R d > 20 mm) and condition-C rainfall events (R d > 580 mm), the value of Nd10 in 2000-2009 was around 5 times that in 1990-1999.The two fit lines in Fig. 12 show that the value of Nd10 during 2000-2009 (with the coefficient of determination, R 2 = 0.92) was around 3-4 times that during 1990-1999 (R 2 = 0.82) at the same value of Nr10 .

The relationship between the probability of debris-flow occurrence and the number of rainfall events
Figure 13 shows the relationship between the ten-yearaverage probability of debris-flow occurrences P10 and the ten-year-average number of rainfall events Nr10 for various excess-rainfall conditions in the two periods 1990-1999 and 2000-2009.The P10 value for each period shows a decreasing trend with an increase in Nr10 .The value of P10 obtained from the 2000-2009 fit line is around 3 to 4 times that during 1990-1999 at the same Nr10 .The occurrence of debris flows depends on having a large amount of loose sediment generated in the watershed and an increasing number of extreme rainfall events.Significant hazardous events, such as Typhoons Herb in 1996, Toraji in 2001 and Morakot in 2009, and the Chi-Chi earthquake, triggered many landslides that produced sediment left on hillsides and in gully beds, which provided loose material for the initiation of debris flows.The loose sediment caused by typhoons and the earthquake was concentrated after 2000; this, combined with a large number of extreme rainfall events with R d > 580 mm (Fig. 11), resulted in numerous debris flows during the last decade (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009).Consequently, both the annual average number of rainfall events triggering debris flows Nd10 and the probability of debris-flow occurrences P10 were greater in the last decade than in 1990-1999.

Conclusions
The maximum 24-h rainfall R d was used to analyze the trends in the number of rainfall events related to debrisflow occurrence in the Chenyulan stream watershed.Three rainfall conditions related to debris-flow occurrences presented in this study are (1) rainfall events of R d > 20 mm, the lower boundary of R d for rainfall events ever triggering debris flows during the period 2000 to 2004, the 1999 Chi-Chi earthquake affected period; (2) rainfall events of R d > 230 mm, the lower boundary of R d for rainfall events ever triggering debris flows during the period 1985 to 1999, prior to the 1999 Chi-Chi earthquake; and (3) rainfall events of R d > 580 mm, the lower boundary for extreme rainfall triggering numerous debris flows.
The Chi-Chi earthquake significantly reduced the amount of rainfall required to trigger a debris flow.The rainfall events associated with debris-flow occurrences resulting from the Chi-Chi earthquake mainly occurred in the period 2000-2004, the five years after the earthquake, and these debris flows were triggered by rainfall events with R d > 20 mm.For R d > 20 mm, the average number of rainfall events triggering debris flows and the average probability of debris flows within a five-year period, namely Nd5 and P5 , respectively, during the Chi-Chi earthquake-affected period (2000)(2001)(2002)(2003)(2004) were greater than those during other periods at the same Nr5 (the average number of rainfall events within a five-year period).The average number of rainfall events triggering debris flows (the value of Nd5 for R d > 20 mm) during the earthquake-affected period was 3.8 times that during the five-year pre-earthquake period (1995)(1996)(1997)(1998)(1999); the average probability of debris-flow occurrences ( P5 ) during the earthquake-affected period was 5.5 times that during the fiveyear pre-earthquake period.For R d > 20 mm events, the influence of Nr5 on the values of Nd5 was not significant.For R d > 230 mm and R d > 580 mm events, the values of Nd5 tended to increase with an increase in Nr5 and all events with R d > 580 mm triggered debris flows.
The variations in the average number of rainfall events, the average number of rainfall events triggering debris flows, and

Fig. 1 .
Fig. 1.Locations of debris flows and meteorological stations in Chenyulan stream watershed

Fig. 2 .
Fig. 2. Variations in 5-yr-moving average annual rainfall and rainyseason rainfall (May to October) at three local rainfall stations and the regional average rainfall for the whole Chenyulan stream watershed.

Figure 3 :
Figure 3: Maximum 24-h rainfall d R (mm) during any rainfall event that triggered debris flows over past decades.

Fig. 3 .
Fig. 3. Maximum 24-h rainfall R d (mm) during any rainfall event that triggered debris flows over past decades.
3. They are (1) condition A: R d = 20 mm, which is the lower boundary of the values of R d in Fig.3for the period 1999-2004; (2) condition B: R d = 230 mm, which is the Annual number ( ) of rainfall events with maximum 24-h rainfall greater than 20 mm.Annual number ( ) of rainfall events with maximum 24-h rainfall greater than 20 mm that triggered debris flows.Annual average probability (P) of debris-flow occurrence for rainfall events with maximum 24-h rainfall greater than 20 mm.

Figure 4 :Fig. 4 .
Figure4: Number of annual rainfall events, number of annual rainfall events that triggered debris flow, and annual average probability of debris-flow occurrence for rainfall events with maximum 24-h rainfall greater than 20 mm. 3 Fig.4.Number of annual rainfall events, number of annual rainfall events that triggered debris flow, and annual average probability of debris-flow occurrence for rainfall events with maximum 24-h rainfall greater than 20 mm.

Fig. 7 .
Fig.7.Number of annual rainfall events N r , number of annual rainfall events N d that triggered debris flows, and annual average probability of debris-flow occurrence P for rainfall events having maximum 24-h rainfall larger than 230 mm.

Fig.
Fig.8.Relationship between the five-year-average number of rainfall events that ever triggered debris flows N d5 and the five-yearaverage number of rainfall events N r5 for rainfall events having maximum 24-h rainfall larger than 230 mm.
Number of annual rainfall events having maximum 24-h rainfall larger than 580 mm.Number of annual rainfall events that triggered debris flows for rainfall events having maximum 24-h rainfall larger than 580 mm.Annual average probability of debris-flow occurrence P for rainfall events having maximum 24-h rainfall larger than 580 mm.Number of annual rainfall events , number of rainfall events that triggered debris flows, and annual average probability of debris-flow occurrence r N d N

Fig. 11 .
Fig.11.Variations in ten-year average number of rainfall events N r10 with R d greater than rainfall thresholds R dc , such as R dc = 20, 100, .., and 580 mm, during the periods1990-1999 and 2000-2009.

Figure 13 :
Figure 13: Relationship between the ten-year-average probability of debris-flow occurrence 10 P and the ten-year-average number of rainfall events 10 r N with greater than various rainfall thresholds , such as = 20, 100, .., and 580 mm, during the periods 1990-1999 and 2000-2009.d R of debris-flow occurrences in each decade, namely Nr10 , Nd10 , and P10 , respectively, were analyzed.The value of Nr10 for R d > 100 mm within the last decade(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009) was higher than that during 1990-1999.The increase in Nr10 during the last decade resulted in an increasing frequency of rainfall events triggering debris flows.The average number of rainfall events triggering debris flows Nd10 and the average probability of debris-flow occurrences P10 during the period 2000-2009, increased 3 to 4 times relative to those of the period 1990-1999 at the same Nr10 .The increases in Nd10 and P10 during 2000-2009 may be related to abundant loose sediment caused by typhoons and the Chi-Chi earthquake after 2000 and the increased number of extreme rainfall events (R d > 580 mm) that caused numerous debris flows during the last decade.